Reduce to lowest terms: $ \dfrac{5}{2} \div - \dfrac{5}{7} = {?}$
Answer: Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $- \dfrac{5}{7}$ is $- \dfrac{7}{5}$ Therefore: $ \dfrac{5}{2} \div - \dfrac{5}{7} = \dfrac{5}{2} \times - \dfrac{7}{5} $ $ \phantom{ \dfrac{5}{2} \times - \dfrac{7}{5}} = \dfrac{5 \times -7}{2 \times 5} $ $ \phantom{ \dfrac{5}{2} \times - \dfrac{7}{5}} = \dfrac{-35}{10} $ The numerator and denominator have a common divisor of $5$, so we can simplify: $ \dfrac{-35}{10} = \dfrac{-35 \div 5}{10 \div 5} = -\dfrac{7}{2} $